## The estimation of a random coefficient AR(1) process under moment conditions.(English)Zbl 0573.62086

Let $$x_ k=(\theta +b_ k)x_{k-1}+\epsilon_ k$$, where $$\theta$$ is a constant and $$(b_ k)$$, $$(\epsilon_ k)$$ are independent sequences of random variables with zero mean, independent also of each other. Then $$(x_ k)$$ is a random coefficient AR(1) process.
The author proves strong consistency and asymptotic normality of estimators of parameters of the process $$(x_ k)$$ under conditions which concern only some moments. The proofs are based on martingale differences and they do not need the usual assumptions of strict stationarity and ergodicity.
Reviewer: J.Anděl

### MSC:

 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62F12 Asymptotic properties of parametric estimators